Sacramento daily record-union. [volume] (Sacramento [Calif.]) 1875-1891, 1887-09-24
STRANGE MENTAL FEATS.
SOME MARVELLOUS D0ISGS OF
CALCULATING BOYS.
The Wonderfully Rapid Mental
Work of Colburn. as also
Stafford and Bidder.

more than even the great mental achieve
ments in which mankind Justly take most
pride. The work of Newton differs in
degree only, not in kind, from the work of
q Galileo or Haley; and Newton him
self has told Us that he accomplished his
work, not Il rough some exceptional quail
ity in his powers, but by the patient " in
tention" of his mind for weeks and months
on the subject he sought to master Even
the poetry Of Homer, ola Dante, a Shakes
peare, or Milton Is but the best Of its
kind, not suggestive of abnormal mental
powers. There are mental feats, however.
far less than these achievements of great
minds, far less valuable TO humanity.
which nevertheless suggest much more
striking possibilities. They seem to indi-
cate peculiarities of brain structure com
parable with those casual peculiarities
which biologists call "sports," as the long
backs Of the Ancon sheep, the occasional
appearance of six fingers and toes in the
human race, and the like The recent
recognition Of the influence OF heredity in
mind and character Is well as in BODY.
gives singular interest 10 mental feats such
a | am about to consider, since they sllg-
gest possible developments of brain fInc-
tons by which men may hereafter obtain
mastery over problems at present beyond
their power. In particular / would call
attention TO the evidence which some of
these feats afford of combined powers of
ready apprehension and perfect retention,
which, were they possessed generally by
tse students Of science. would enable them
TO range much more widely over the ever
increasing domain Of knowledge than even
the most skillful among them can al pres
ent
From this point of view the wonderful
powers which have been displayed by "cal-
culating boys" deserve special attention.
Newton was slow in calculation and he
labored, as it were, to fix his attention on
the subjects to which his calculations re-
lated. How marvelously would those
higher mental powers Of his which raised
him above all the thinkers in his own line
have been aided had he possessed the swift
and accurate calculating powers of Zerah
Colbum or a George Bidder, and their
amazing power of retaining in their minds
almost without effort, long arravs-or
rather large groups-of numbers The
calculating feats of these lads and of some
Others, seemed 1t first so marvellous that
the idea WIS suggested that they employed
some new process, akin perhaps to the use
Of logarithms by the calculator who works
with pen and paper and book Of tabular
statements. But Zerah Colburn twho out
cfAa L. .l,rF,sf
almost as ignorant as Blind Tom). could
reply only to questions about his methods,
" God put these things into my head
cannot put them into yours Bidder was
able to explain very fully his methods by
which he made his rapid calculations; and.
so far from diminishing the marvel his ex-
PLANTATION added 10 il. For it showed that
he went through processes, each one of
which requires careful work and the reten-
ton OF many groups OF numbers and this
with rapidity incomparablv greater than
that with which the most practiced COM
puter could deal with them on paper. nav.
very much faster than thev could have
been set down from dictation.
Let us consider few of the feats of the
calculating boys
Zerah Colburn was asked TO say what
number multiplied twice into itself would
give the number 26S, 33G,I25. The idea
was to see how far he would get ahead of
practiced computer, who was set to work
finding the cube root OF the number for
that was what Colburn was asked for by
the usual process. But before the prac-
ticed compuier had written down the num-
her, Colburn gave the number, 645. Col
burn was at this time only eight wears old
and he had not even so much instruction
in arithmetic rs most boys of that age
have received. He knew nothing of the
rules for extracting roots. But even if he
had known how to extract the cube root
OF number, his feat could not he les
marvellous. Let any one who would learn
10 appreciate COlburn's calculating power
Try the following experiment: Set down
the number just named and obtain the
cube root by the ordinary method, making
no hurry over the work; next copy the
figures thus obtained, setting them down
lin their order rs obtained as fast as a
pen or pencil viii travel, noting the time
taken in this easy part Of the work. Then
consider that a child eight wears old Oh
tanned the right result, without pen or
pencil, in less time than had been taken 10
copy down the number itself to which all
the calculation thus written ont had been
applied.
Asked what numbers viii divide 36,0S3
exactly. Colburn 1t once answered " None"
Let the reader try how long it takes with
pen and paper 10 prove that this Is really
so. He viii have to try the divisions 3, :.
II, IS, Il, 70, %. %, 81, 81. Il, II, Il, -,
and many more, up to Isl, before the proof
wild lie complete.
Once, and once only, did CoIburn have
to make any considerable effort IN dealing
with 4 number As he had dealt with So
OS3. The number was somewhat famous
IN mathematical aunals-viz: 4.294.957.-
297, Of which the great arithmetician Fer
mat declared that il had no division.
Fermat even gave what appeared TO him a
proof Of this, bat the celebrated mathema-
tician Euler showed that the proof was in
complete. Euler also after long labor,
found 4 number, GAL. which will divide
Fermat's asserted "indivisible" Colburn
was set the same task which had foiled
Fermat, and had occupied Euler for
months. The little child could not an
swer thai day, nor the next, nor for week
or fortnight. but in the third week he gave
the solution. During that time he had
kept no records of his work save in that
wonderfully retcntiye little brain Of his.
II may interest the reader 10 know that
the number over which Fermat and Euler
had contended Is obtained by multiplying
two into itself thirty one times and adding
units. Col5arn did the work of thus OBJ
tanning the number in q few minutes.
Bidders feats acquire additional interest
from the circumstance that he was ableto
explain precisely the methods by which he
worked. | once had a conversation with
Professor Stafford, who had been for 4 long
while known Is . calculating bow" about
the method he used He admitted that
his ideas on this point were somewhat
vague. lie found, however, that his mind
had 4 tendency, apart from any question
ing 10 turn TO the study Of numbers, and
that when any number was named or
thought Of, he fell half uneonsciouslv into
the work Of mentally resolving II If it
admitted of resolution into factors. Posi-
bly, this mental tendency. accompanied bv
an abnormal power Of recollecting num-
hers, might have helped Stafford, and before
him Colburn, In obtaining results quickly. |
because already immense numbers in null
Implications and divisions had been nen-
tally recorded and were thus as ready for
application as with most Of Us Is the multi
picatiou table. But this was not the way